Don’t private jets typically fly out of different airfields than public commercial flights?

It's a mixed bag. At least some private planes fly out of at least some airfields that also have public commercial flights. The airport I am most familiar with, Salt Lake International, has a private-plane facility. The private planes typically use runways that are not often used by commercial jets, but they still use the same airspace.

That must be the reason the Democrats just agreed to end the shutdown without negotiation.